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Is "So if there are 23 people in a room there's a 50% chance that one of them will share a birthday with me?" correct? If you pick a fixed person (you) that wo

by pendext 14y ago

Is "So if there are 23 people in a room there's a 50% chance that one of them will share a birthday with me?" correct? If you pick a fixed person (you) that would break the pigeonhole principle, I think. I would think that saying "So if there are 23 people in the room there is a 50% chance any 2 of those people share the same birthday" is better. Edit: I misunderstood, you're saying that other people are misunderstanding. My mistake!

ColinWright 14y ago
You're misquoting or misunderstanding. The comment to which you are replying said: The paradoxy bits of the problem are the things that people find confusing. "Only 23?!" or "So if there are 23 people in a room there's a 50% chance that one of them will share a birthday with me?" In that comment he is saying that people mis-understand the question, and assume that it means that once there are 23 people in the room, then there's a 50:50 chance they will share a birthday with them specifically. And that's exactly the wrong question, as you point out. So when you say: Is "So if there are 23 people in a room there's a 50% chance that one of them will share a birthday with me?" correct? No, that's not correct, but it is what people think they hear, and it's that confusion that makes this whole thing sometimes called a paradox. So let's be clear: If you're in a room with 22 other people, the chance that one of them shares a birthday specifically with you is nowhere near 50% However, the chance that among the 23 people in the room there is, somewhere, a shared birthday, is indeed slightly greater than 50% And my experience is that it really doesn't matter how carefully you word this, some people simply will not understand it.
- pendext 14y ago
  You're right, I misunderstand the comment I replied was using that as an example of how other people misunderstand the problem. D'oh. Edited!

by pendext 14y ago

ColinWright 14y ago

You're misquoting or misunderstanding. The comment to which you are replying said: The paradoxy bits of the problem are the things that people find confusing. "Only 23?!" or "So if there are 23 people in a room there's a 50% chance that one of them will share a birthday with me?" In that comment he is saying that people mis-understand the question, and assume that it means that once there are 23 people in the room, then there's a 50:50 chance they will share a birthday with them specifically. And that's exactly the wrong question, as you point out. So when you say: Is "So if there are 23 people in a room there's a 50% chance that one of them will share a birthday with me?" correct? No, that's not correct, but it is what people think they hear, and it's that confusion that makes this whole thing sometimes called a paradox. So let's be clear: If you're in a room with 22 other people, the chance that one of them shares a birthday specifically with you is nowhere near 50% However, the chance that among the 23 people in the room there is, somewhere, a shared birthday, is indeed slightly greater than 50% And my experience is that it really doesn't matter how carefully you word this, some people simply will not understand it.

pendext 14y ago
You're right, I misunderstand the comment I replied was using that as an example of how other people misunderstand the problem. D'oh. Edited!